Ministers are considering a new wave of publicly funded housebuilding to kick-start the ailing construction industry and ease the shortage of homes.

The housing minister, Grant Shapps, indicated his support for recommendations in a new government-commissioned report into the housing shortage which also proposes relaxing planning regulations that require developers to include social housing and allowing private investors to build on public land at no initial cost. The moves are designed to encourage a new round of construction, with taxpayers reaping the benefits when the homes are sold.

The report, commissioned by the government from the chairman of the 3i investment group, Sir Adrian Montague, and published on Thursday, will be taken even more seriously because of the urgent need for a boost to the economy to create jobs and confidence in the private sector.

Montague estimates that housing demand is increasing each year at double the rate at which homes are being built. "Sir Adrian Montague's findings offer both a blueprint for achieving this goal [more housebuilding], and for setting the standards of accommodation that people should expect," said Shapps. "I will be considering his recommendations very carefully."

The suggestion that councils could relax affordable home requirements in planning deals for developers – to make projects more affordable when banks are reluctant to lend money – will be controversial because of the impact on people on low incomes.

Labour said the report failed to address rocketing rents in existing homes. The shadow housing minister, Jack Dromey, said: "As rents hit a record high in July, the government should be acting to address this problem, not looking for ways to water down existing legislation, which could make the problem worse."

Mike Jones, chairman of the Local Government Association's environment and housing boards, said: "Any strategy to boost the number of new rental homes should not come at the expense of new affordable housing, and councils will in consultation with their residents always seek to ensure a suitable balance between the need for private rental property and new affordable homes."

Montague's report says the number of families renting has mushroomed from 2 million in the 1980s to 3.8 million. It says more families are staying in rented accommodation for longer before they can afford to buy property.

He recommends that local authorities make fewer demands in return for planning permission and review conditions attached to developments that already have planning permission but have stalled over cost concerns. In return, councils could impose other conditions on owners, for example that new homes have to be available to rent for 10-21 years.

The report says the government and local authorities could donate land or even funding to reduce the initial outlay, and so the risk, for developers, in return for a share of the profits when schemes are sold, usually to big institutions such as pension funds which want a steady return for investors.

Montague also suggests a taskforce to co-ordinate the government's initiatives. More controversially, he rejects a "kitemark" for standards in rented homes but suggests a voluntary code of conduct for accommodation, energy efficiency, repairs and management.

Campbell Robb, chief executive of the housing and homelessness charity Shelter, said: "While we welcome the report's recognition of the need for more and better quality homes for people to rent, it misses a trick in offering nothing for the millions of people already in the sector, paying sky-high rents and living under constant threat of eviction or further rent rises."